In Texas (a community property state), is there a way for a person to buy or own property to which to a spouse will have no right?
To buy? In all likelihood, no. Community property state laws generally state that property (not just real property) acquired during a marriage becomes part of the "community" (the community of the two spouses) and is usually divided 50/50 in the instance of a divorce. Laws may vary by state on how that property is divided, though. For example, California does 50/50, equally, whereas Texas does it "equitably."
Factors Used in Equitable Distribution:
If you live in a state using the equitable distribution doctrine, the main factors are each spouses earning capacity on their own, if and which parent is the legal caretaker of the children if there are children, and whether there are any examples of specific fault for the divorce, such as adultery, abuse, etc.
More granular factors related to the main ones include whether someone would lose a benefit or mode of compensation they would have been entitled to if the marriage continued; health matters; age differences and how they may relate to ability to maintain employment or receive benefits; what size inheritance, if any, a spouse may be positioned to receive; and the size of the estate itself.
Community Property or Not:
If the property is acquired while you are married, it is generally considered community property (this is true often in states that don't have community property statutes, but especially so in those that do). This includes income, real or personal property acquired with income earned during the marriage (cars, houses, luxury items, appliances, etc.), as well as debts.
Conversely, property you had before you got married, property you acquired after you and your spouse became legally separated, and any property received as a gift or as an inheritance from a third party remains separate after divorce. On the latter item, the party that received the gift or inheritance must keep it separate during the marriage in order for it to remain separate. If you receive a cash inheritance, don't dump it into your joint bank account, or you will likely have waived your separate claim to it.
This website provides some common examples and their dispositions as separate property or community property toward the bottom of the page: http://www.nolo.com/legal-encyclopedia/separate-community-property-during-marriage-29921.html.
After @ohwilleke's helpful comment below about the post-nup, I'm adding the following.
A couple may create a transmutation agreement, which is a type of post-nuptial agreement. A transmutation agreement operates in a community property state to keep the two spouse's property separate despite the state law (it is worth noting, this is similar to the principle of contract law where parties to a contract usually are able to waive certain rights guaranteed them in statute assuming the waiver was made knowingly and willingly). It is recommended that both spouse's acquire separate counsel so as to ensure both spouse's are fully aware of the potential outcomes of the agreement. That will protect the agreement from being challenged by one of the spouse's later.